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# Strong nuclear force vs binding energy watch

1. Hello everyone
So I came across this scentence in my textbook which I found a bit confusing and would like some help please.
It said " Note that binding energy is not the energy holding the nucleus together- be careful when defining this term"
Since the binding energy is the work done to separate the nucleons wouldn't that mean that it equals the energy caused by the strong nuclear force that hold the nucleons together? But the statement says otherwise.
Any help is really appreciated thanks
2. Binding energy isn't physically an energy that holds something together, I mean, to my understanding. Here's how I think about it:

The nucleons in the nucleus are held together by the strong force, which in essence creates a potential well, which these nucleons lie within.
To escape, work must be done on them, work that pulls them out of the potential well they lie in.
The potential well itself could be described by a graph, describing potential energy as a function of X/radial distance, whatever you might have, for an electron it's generally radial distance but in this case it'd be more complicated seeing as you may well have many nucleons, etc. Either way, just look at my terrible drawing :P (it's er... a helium nucleus, just to show the forces involved... pretty bad. I know. Ignore gravity!!)

The nucleons may have to contend with electrostatic repulsion, or not, either way, the strong force binds them here with a potential well that may be similar to that one I drew. Either way, by convention (at least what I was taught) the potential is negative when bound. Idk about your exam board, so make sure to check ;-;

In effect, it's true that the energy could be considered to be holding them together, but, the energy doesn't hold them together, it isn't a force/etc, it's just the energy that binds them in this potential well they occupy, their potential energy. To escape this potential well, work must be done, positive work, thus a positive force, one that takes them out of the well, reducing the magnitude of the potential energy as they move farther out (for this example I drew).

Either way, it's all down to convention. I know that for my exam this year, we were told the stuff I just wrote down above, that the nucleons, electrons, whatever particle may occupy the potential well, is bound by the forces in the interaction and not by the energy, and we can't actually say that the energy is what binds them. It's more-so a lack of the energy required to escape the potential well. I also know that for my AQA exams last year we were taught to say a similar thing, though I don't know if that was the actual way to go about it.
3. (Original post by Pinkycherry)
Hello everyone
So I came across this scentence in my textbook which I found a bit confusing and would like some help please.
It said " Note that binding energy is not the energy holding the nucleus together- be careful when defining this term"
Since the binding energy is the work done to separate the nucleons wouldn't that mean that it equals the energy caused by the strong nuclear force that hold the nucleons together? But the statement says otherwise.
Any help is really appreciated thanks

I think the sentence of "Note that binding energy is not the energy holding the nucleus together - be careful when defining this term" is trying to warn the readers or students of not associating binding with holding something in the definition.

Energy is a quantitative measurement of the amount work to be done on a system. Thus, energy should not be considered as holding the nucleons in the nucleus together because it is the nuclear force that is holding or binding the nucleus together.

If you want to borrow the concepts of bonding form and bond breaking to explain about binding energy, you need to be careful.

To form a nucleus, say a 4He nucleus, we need to extract out energy that is equal to the magnitude of the binding energy from a system 2 individual protons and 2 individual neutrons before binding them 2 protons and 2 neutrons together to form the 4He nucleus. This means that the energy is released when the nucleus is formed from separate nucleons.

Instead of thinking energy caused by the nuclear force, you can think in terms of association as there is no cause and effect:

Binding energy is the energy associated with the nuclear force that holds the nucleons together or a measure of the work/energy that the nuclear force needs to do to separate the nucleus into individual separate nucleons.
4. (Original post by Callicious)
Binding energy isn't physically an energy that holds something together, I mean, to my understanding. Here's how I think about it:

The nucleons in the nucleus are held together by the strong force, which in essence creates a potential well, which these nucleons lie within.
To escape, work must be done on them, work that pulls them out of the potential well they lie in.
The potential well itself could be described by a graph, describing potential energy as a function of X/radial distance, whatever you might have, for an electron it's generally radial distance but in this case it'd be more complicated seeing as you may well have many nucleons, etc. Either way, just look at my terrible drawing :P (it's er... a helium nucleus, just to show the forces involved... pretty bad. I know. Ignore gravity!!)

The nucleons may have to contend with electrostatic repulsion, or not, either way, the strong force binds them here with a potential well that may be similar to that one I drew. Either way, by convention (at least what I was taught) the potential is negative when bound. Idk about your exam board, so make sure to check ;-;

In effect, it's true that the energy could be considered to be holding them together, but, the energy doesn't hold them together, it isn't a force/etc, it's just the energy that binds them in this potential well they occupy, their potential energy. To escape this potential well, work must be done, positive work, thus a positive force, one that takes them out of the well, reducing the magnitude of the potential energy as they move farther out (for this example I drew).

Either way, it's all down to convention. I know that for my exam this year, we were told the stuff I just wrote down above, that the nucleons, electrons, whatever particle may occupy the potential well, is bound by the forces in the interaction and not by the energy, and we can't actually say that the energy is what binds them. It's more-so a lack of the energy required to escape the potential well. I also know that for my AQA exams last year we were taught to say a similar thing, though I don't know if that was the actual way to go about it.
Thank you so much this really helped and yes it is negative in the spec am doing( ocr btw) Can you please explain to me how you used differentiation to get a negative sign for the repulsive and positive for attractive.
5. (Original post by Eimmanuel)
I think the sentence of &quot;Note that binding energy is not the energy holding the nucleus together - be careful when defining this term&quot; is trying to warn the readers or students of not associating binding with holding something in the definition.

Energy is a quantitative measurement of the amount work to be done on a system. Thus, energy should not be considered as holding the nucleons in the nucleus together because it is the nuclear force that is holding or binding the nucleus together.

If you want to borrow the concepts of bonding form and bond breaking to explain about binding energy, you need to be careful.

To form a nucleus, say a 4He nucleus, we need to extract out energy that is equal to the magnitude of the binding energy from a system 2 individual protons and 2 individual neutrons before binding them 2 protons and 2 neutrons together to form the 4He nucleus. This means that the energy is released when the nucleus is formed from separate nucleons.

Instead of thinking energy caused by the nuclear force, you can think in terms of association as there is no cause and effect:

Binding energy is the energy associated with the nuclear force that holds the nucleons together or a measure of the work/energy that the nuclear force needs to do to separate the nucleus into individual separate nucleons.
Thank you for the explanation. I guess I knew it was the force that hold the nucleons together not the energy but was wondering that the binding energy should equal the work done by the strong force( if that's correct) to hold the nucleons together and so the binding energy and strong nuclear force are proportional?
6. (Original post by Pinkycherry)
Thank you for the explanation. I guess I knew it was the force that hold the nucleons together not the energy but was wondering that the binding energy should equal the work done by the strong force( if that's correct) to hold the nucleons together and so the binding energy and strong nuclear force are proportional?
“…but was wondering that the binding energy should equal the work done by the strong force(if that's correct) to hold the nucleons together…”

I don’t think it is right to say “work done by the nuclear force to hold the nucleons together”. It is the phrase “to hold the nucleons together” that make it incorrect. We don’t need to do work done to bind two objects together, but we need to do work to bring two objects close together. Be careful about the usage, you can be penalized in A level exam.

In my previous post, I mention that “Binding energy is a measure of the work that the nuclear force needs to do to separate the nucleus into individual separate nucleons.” , which you can also say that “Binding energy is a measure of the work that the nuclear force needs to do to form the nucleus from the separate nucleons”.
OR (if you like)
(Negative) Binding energy is the work done by the nuclear force to form the nucleus from the separate nucleons. I include negative because when the nucleons come together to form the nucleus, there is a decrease in nuclear potential energy and binding energy is taken to be positive by convention.

“so the binding energy and strong nuclear force are proportional?”

I don’t know. I don’t think we have known how to write an explicit form of nuclear force which looked like gravitational force or electric force that you have learned in A-level.

Nuclear force is a more complicated force. As I can recall from my uni study long time ago, it seems to be a three-body (or four-body) force rather than a two-body force that look like gravitational force.
Unless you are taking Yukawa potential as a “good model” to describe the nuclear force that you are interested in. You can read Wikipedia on the nuclear force.
https://en.wikipedia.org/wiki/Nuclear_force

Side note : You better check with your teacher in regard to the phrase "strong nuclear force" whether the examination board allow you to use, when you are talking about nucleon-nucleon interaction in nucleus. When strong nuclear force is used, it means strong interaction but it is not the nuclear force that we are talking about in a typical nuclear physics chapter.
7. (Original post by Eimmanuel)
“…but was wondering that the binding energy should equal the work done by the strong force(if that's correct) to hold the nucleons together…”

I don’t think it is right to say “work done by the nuclear force to hold the nucleons together”. It is the phrase “to hold the nucleons together” that make it incorrect. We don’t need to do work done to bind two objects together, but we need to do work to bring two objects close together. Be careful about the usage, you can be penalized in A level exam.

In my previous post, I mention that “Binding energy is a measure of the work that the nuclear force needs to do to separate the nucleus into individual separate nucleons.” , which you can also say that “Binding energy is a measure of the work that the nuclear force needs to do to form the nucleus from the separate nucleons”.
OR (if you like)
(Negative) Binding energy is the work done by the nuclear force to form the nucleus from the separate nucleons. I include negative because when the nucleons come together to form the nucleus, there is a decrease in nuclear potential energy and binding energy is taken to be positive by convention.

“so the binding energy and strong nuclear force are proportional?”

I don’t know. I don’t think we have known how to write an explicit form of nuclear force which looked like gravitational force or electric force that you have learned in A-level.

Nuclear force is a more complicated force. As I can recall from my uni study long time ago, it seems to be a three-body (or four-body) force rather than a two-body force that look like gravitational force.
Unless you are taking Yukawa potential as a “good model” to describe the nuclear force that you are interested in. You can read Wikipedia on the nuclear force.
https://en.wikipedia.org/wiki/Nuclear_force

Side note : You better check with your teacher in regard to the phrase "strong nuclear force" whether the examination board allow you to use, when you are talking about nucleon-nucleon interaction in nucleus. When strong nuclear force is used, it means strong interaction but it is not the nuclear force that we are talking about in a typical nuclear physics chapter.
Thank you so much that really helps. I don't actually have a teacher I study independently so I mainly rely on what is written in the spec's textbook. Thanks again for you help

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